MATHCOUNTS State Target 2025 (Problem 6)
CombinatoricsHard
Chandra writes down all of the nonempty subsets of , and for each subset she then erases everything except the largest element. What is the mean value of all of these largest elements? Express your answer to the nearest integer.
Instead of considering the subsets, consider the elements.
In how many of the subsets is element the maximum element?
When is the maximum element of a subset, then should be in the subset. should not be in the subset; otherwise, is not the maximum element. can either be in the subset or not.
So we consider elements respectively
times.
times.